[2010] Correlation Analysis of Financial Contagion

8/8/2019 [2010] Correlation Analysis of Financial Contagion

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Correlation Analysis of Financial Contagion*

GIANCARLO CORSETTI

University of Cambridge, University of Rome III and CEPR

MARCELLO PERICOLI

Bank of Italy

MASSIMO SBRACIA

Bank of Italy

JULY 2010

PRELIMINARY VERSION

1. INTRODUCTION

The outbreak of the Greek crisis in 2009-2010 and the transmission of financing strains to

other countries such as Portugal, Ireland, and Spain have once more turned the spotlight

on financial contagion. The term contagion, generally used in contrast to interdependence,

conveys the idea that during financial crises there might be breaks or anomalies in the

international transmission mechanism, arguably reflecting switches across multiple equilibria,

market panics unrelated to fundamentals, investors herding and the like.

There is still wide disagreement among economists about what contagion is exactly, and

how it should be tested empirically. Pericoli and Sbracia (2003), for instance, list five different

definitions and related measures of contagion that are frequently used in the literature.1

A

common approach, however, consists of identifying breaks in the international transmission of

shocks indirectly, inferring them from a significant rise in the correlation of asset returns across

markets and countries. In practice, analysts compare cross-country and cross-market

correlations of asset returns in tranquil and crisis periods, under the maintained assumption

that a significant rise in the correlation of returns can be attributed to a break in their data-

generating process. Of course, the importance of the correlation statistics for financial investors

*Paper prepared for the book: Robert W. Kolb (ed), Financial Contagion: The Viral Threat to the Wealth of

Nations, Wiley: NY (forthcoming). The views expressed in this paper are those of the authors and do notnecessarily reflect those the Bank of Italy or of any other institution with which the authors are affiliated.


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provides a strong and direct motivation for this type of analysis. As Engle (2009) puts it, the

correlation structure of financial assets is the key ingredient to a portfolio choice, because it is

instrumental in determining the risk.

Still, these studies share a basic problem. Crises are typically identified as periods in

which return volatility is abnormally high. Suppose that a crisis is driven by large shocks to a

common factor, affecting all asset returns across the world. Other things equal, a higher

variance of the common factor simultaneously causes higher-than-usual volatility andstronger

comovements in all markets. In other words, holding the parameters of the data-generating

process constant (other than the variance of the common factor), so that by definition there is

no break in the international transmission of financial shocks, a rise in the magnitude of the

common shock mechanically increases cross-country correlations. Consistently with most

definitions, however, this would provide no evidence of financial contagion. Meaningful tests

of contagion should thus net out the effect of changes in volatility from changes in cross-

country correlations.

In this chapter, we first document a small set of stylized facts that motivates the

construction of tests of contagion based on correlation analysis (Section 2). Second, drawing

on Corsetti et al. (2005), we present a general correlation test for contagion addressing the

issue discussed above, and illustrate its properties with an application to the Hong Kong stock

market crisis of October 1997 (Section 3). Section 4 concludes.

2. STYLIZED FACTS

We start by documenting a set of four stylized facts characterizing the transmission of

shocks across stock markets. The first two are well understood in the literature: (i) sharp drops

in stock prices tend to cluster across countries, and (ii) the volatility of returns rises during

financial crises. The other two are often confused in formal and informal discussions of


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contagion: (iii) financial crises are frequently associated with a rise in the cross-country

covariances of returns; (iv) cross-country correlations of returns increase often during financial

turbulences, but there are many crisis episodes in which correlations fall or remain invariant,

relative to tranquil periods.

We document these facts, using weekly stock prices and returns in local currency for 20

countries: the G7, Argentina, Brazil, Mexico, Greece, Spain, Russia, Hong Kong, Indonesia,

South Korea, Malaysia, Philippines, Singapore, and Thailand. The sample period runs from

January 1990 to May 2010. The data source is Thomson Reuters Datastream.

Sharp falls in stock prices tend to occur in clusters across national markets

Crises are not independently distributed. As noted by Eichengreen et al. (1996), for

instance, long phases of tranquility in foreign exchange markets are interrupted by waves of

speculative attacks, simultaneously hitting different currencies. Similar patterns characterize

stock markets. This is apparent in the two decades spanning the period 1990-2010 (fig. 1). In

five episodes of financial turmoil, at least of the countries in our sample recorded a decline

in stock market prices by 20 percent or more. These episodes are the U.S. recession in 1990-

1991, occurring contemporaneously to the First Gulf War; the Russian financial crisis and the

associated collapse of the U.S. hedge fund LTCM in 1998; the U.S. recession in 2001 and the

terrorist attacks on September 11; the period preceding the Second Gulf War; the Great

Recession of 2008-2009. In other three episodes, the financial turmoil was somewhat less

widespread: the crisis of the European Exchange Rate Mechanism (ERM) in 1992 (which

nonetheless affected stock prices in Europe, Asia and Latin America); the crisis in Mexico in

1994-1995; and the stock market crash in Hong Kong in October 1997. It is worth emphasizing

that the last two crises severely affected stock prices all over the world, even though they

originated in two peripheral economies.


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The volatility of stock market returns rises during crisis periods

The major crisis episodes in our sample are characterized by a sharp increase in the

volatility of returns (fig. 2). Among them, the Great Recession of 2008-2009 stands out for

both its virulence and global nature. In fact, following a period of very low volatility in asset

prices between 2004 and 2007 (below 15%), volatility rose to unprecedented levels (up to over

40% for the cross-country median), affecting most countries, as shown by the small

interquartile difference.

Covariances between stock market returns frequently increase during crisis periods

The covariances of returns display a somewhat different pattern relative to volatility (fig.

3). A sharp rise in the covariances is apparent during the crisis episodes in 1990-1991, in 1998,

in 2001, and especially during the Great Recession. A clear rise in covariances also occurred

during the collapse of the Hong Kong stock market in 1997, as well as during the burst of the

dot-com bubble in March 2000. But there is virtually no rise in covariances during the ERM

crisis or during the Mexican crisis in 1995. Note that covariances remained on a descendent

path after September 11, until the eruption of the global crisis in 2007.

Correlations often rise during crises, but are not always higher than in tranquil periods

Looking at the major crisis episodes listed above, a clear rise in correlations can be

detected in 1990-1991, during the Mexican crisis in 1995, during the Hong Kong stock market

crash in October 1997, in 1998, and during the Great Recession (fig. 4). Correlations instead

declined in 1992, during the ERM crisis. In 2001, they rose only after the terrorist attacks of

September 11, although many countries had already recorded sharp falls in stock prices since

the beginning of the U.S. recession in March. By the same token, there was no rise in


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correlation before the Second Gulf War, even if at the end of 2002 more than half of the stock

markets in our sample had already recorded sharp price falls; correlations only started to rise in

February 2003, during the last phase of stock price adjustment, and continued to increase

through the spring of 2004 at a time in which stock prices were already on a rising path.

Note that during the tranquil period 2004-2007, characterized by rising stock prices and

low return volatility, the median correlation is often above the peaks observed in crisis

episodes, such as those recorded in 1998 and in 2001.

3. CORRELATION ANALYSIS OF CONTAGION: THEORY AND AN

APPLICATION

Can we interpret a significant increase in the comovements of asset returns during

financial crises as evidence of contagion? More specifically, can we infer contagion via a

straightforward application of standard statistical tests for differences in correlation

coefficients? As already mentioned, a key problem with this approach is that the correlation

between returns is affected by their volatility, which is typically higher during crises. This

point was acknowledged early on by seminal contributions on contagion, such as King and

Wadhwani (1990).2

To illustrate the problem in detail, assume that returns are generated by a standard factor

model:

ii

jj

fr

fr

++=

++=

10

10,

wherej

r andi

r denote stock market returns, respectively, in countries j and i; f is a global

factor affecting all countries (usually, the market return); j and i are idiosyncratic factors

independent off and of each other; 0 , 0 , 1 and 1 are constants, with the last two


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parameters measuring the strength of cross-country-linkages: the higher 1 and 1 , the stronger

the correlation betweeni

r andj

r . The expressions above can be derived from several models

in finance, including the capital asset pricing model and the arbitrage pricing theory.

From the factor model above, the correlation between ir and jr , hereafter denoted with

, can be written as:

2/1

2

1

2/1

2

1 )(

)(1

)(

)(1

+

+=

fVar

Var

fVar

Varij

.

Here is the problem: depends on the importance of the terms )(21 fVar and )(2

1 fVar ,

capturing how movements in the common factor affect returns, relative to the terms )( jVar

and )(i

Var , reflecting country idiosyncratic noise. Suppose we observe a crisis in country j,

associated with an increase in the volatility of the returns jr . Holding the parameters 1 and

1 constant, the effect of the crisis on the cross-country correlation of returns will depend on

the extent to which the rise in the variance ofj

r is driven by the variance of the common factor

f, as opposed to the variance of the country-specific factor j . If movements in the common

factors are relatively large, the correlation rises; otherwise, it falls. Two points are worth

stressing: correlations may increase or decrease during a crisis, and change with the variance of

jr , even if the intensity of the cross-country linkages 1 and 1 does not change at all. These

observations suggest that, according to the standard definition of contagion, some fluctuations

in correlation are actually consistent with simple interdependence, in the sense that they can

occur absent changes in the parameters of the model. To provide evidence in favor of

contagion, changes in correlation should be large enough, to point to breaks in the transmission

mechanism, i.e. to changes in the structural parameters 1 and 1 , affecting the intensity of the

cross-border transmission of shocks (note that 0 and 0 do not affect ).


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Thus, proper tests of contagion should at least distinguish between breaks due to shifts in

the variance of the common factors, and changes in the values of 1 and 1 . Using the factor

model described above, in Corsetti et al. (2005) we have shown that, under the null hypothesis

of no contagion, the correlation between ir and jr corrected for the increase in the variance of

jr , takes the following form:

( )

2/1

2 11

1

1

1

++

+

+

+=

TC

T

,

where

)|(

)|(2

1 TfVar

TVar jT

= ,

)|(

)|(2

1 CfVar

CVar jC

= ,

)|(

)|(1

TrVar

CrVar

j

j=+ and ( ) 11

11

+

++=

C

T

,

and Tand Cdenote, respectively, the tranquil period (a regime characterized by the absence

of crisis) and the crisis period (a regime of turmoil initiated by the crisis in country j). The

correlation statistic depends on the correlation in the tranquil period (), the change in the

variance ofj

r during the crisis ( ), as well as the relative importance of the idiosyncratic

factor relative to the global factor during the tranquil and the crisis period ( T and C ). Note

that, in the special case in which T and C are identical, T = C = (i.e. in country j the

variance of the country-specific factor relative to that of the common factor remains constant

during the crisis), further simplifies as follows:

( )

2/1

2 11

1

++

+=

.


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Now, by construction, is the correlation under the assumption of interdependence

i.e. the assumption that the intensities of the cross-country links 1 and 1 do not change

between tranquil and crisis periods. Testing for contagion requires verification as to whether

the correlation observed during the crisis, call it c , is significantly larger (or smaller) than .

In other words, instead of comparing c to (a comparison biased by the increase in the

variance ofjr ), a proper test for contagion should compare

c to .

It is important to stress that biases in correlation tests of contagion occur not only if one

fails to correct, but also if one overcorrects the influence of changes in the variances across

regimes. An example of overcorrection can be illustrated as a special case of (or ), by

setting T =C

=0 i.e. by arbitrarily and unrealistically imposing that the returns in the

country where the crisis originates are not hit by any market-specific shock. In this case, the

factor model collapses to an ad hoc linear model iji rr ++= 10 , and the test statistics

becomes

1/2

2

1

1

+ +

. This framework again, a special case of our model for 0)( =jVar

implies that correlation always increases with the variance ofjr , that is, it always increases

during crises. This prediction is clearly inconsistent with the evidence discussed in Section 2.

Most importantly, because of overcorrection, tests derived from this biased framework tend,

not surprisingly, to always yield the same result of no contagion across crisis episodes.

To illustrate our methodology, we reproduce results from early work (see Corsetti et al.

2005), in which we study contagion from the market crisis in Hong Kong in October 1997

an archetype example in the literature. Based on a subset of 18 of the 20 countries in our

sample (excluding Spain and Greece), we compute two-day rolling averages of daily returns in

US dollars between January 1 1997 and October 17 1997 (the tranquil period), as well as

between October 20 1997 and November 30 1997 (the crisis period).3

The latter period starts


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with the crash in the Hong Kong stock index, which lost 25 per cent of its value in just four

days from October 20 onwards. Hong Kong stock prices then continued to decline until the end

of November, seemingly influencing returns in several other markets.

The parameter is estimated by computing the variance of Hong Kong stock returns in

the tranquil and the crisis period. The ratios T and C are obtained by regressing returns on

the Hong Kong stock market on a common factor, which can be proxied by returns on the

world stock market index produced by Thomson Reuters Datastream a weighted average of

the stock indices of several countries. As an alternative, we also use a cross-sectional average

return from the full sample, the G7 countries, or the United States only, and further verify our

results using principal components and factor analysis.

Results are quite striking. Ignoring the need to correct the correlation coefficient, a

standard statistical test of the hypothesis c would reject the null in favor of the alternative

c > for 8 out of 18 countries. Correcting for changes in the variance of returns makes a

difference: using the world stock market index as a benchmark, the hypothesis of

interdependence () is rejected for only 5 countries under the maintained assumption

T = C , and for 6 countries in the general case T C .4

Overcorrection can be quite

misleading though. A test imposing T = C =0 on the data, still popular among practitioners,

would reject interdependence for just one country (Italy).

5. CONCLUSION

Correlation analysis provides a useful tool for testing for financial contagion. Yet, no

correlation measure of interdependence can be derived independently of a model of asset

returns. Analysts should note their preferred model, and verify its implications for correlation

analysis. Specifically, different models may prescribe different corrections of the standard


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correlation coefficient in order to check for changes in the variance of returns across tranquil

and crisis periods. Our results, however, strongly suggest that country-specific noise should not

be arbitrarily ignored in testing for structural breaks in the international transmission of shocks.

REFERENCES

Corsetti G., Pericoli M., Sbracia M., 2005. Some Contagion, Some Interdependence: More

Pitfalls in Tests of Financial Contagion. Journal of International Money and Finance,

Vol. 24, 1177-1199.

Eichengreen B., Rose A., Wyplosz C., 1996. Contagious Currency Crises: First Tests.

Scandinavian Journal of Economics, Vol. 98, 463-494.

Engle R., 2009.Anticipating Correlations: A New Paradigm for Risk Management. Princeton

NJ: Princeton University Press.

King M.A., Wadhwani S., 1990. Transmission of volatility between stock markets.Review of

Financial Studies, Vol. 3, 5-33.

Pericoli M., Sbracia M., 2003. A Primer on Financial Contagion. Journal of Economic

Surveys, Vol. 17, 571-608.

1Pericoli and Sbracia (2003) discuss the fact that some studies do not distinguish between contagion and

interdependence, but focus on the channels through which negative shocks propagate. In these studies, contagion

is defined as an increase in the probability of a crisis following the crisis in another country or as a volatility

spillover. More recently, a new wave of studies has made the distinction between contagion and interdependence

central, and has developed tests of contagion based on regime switching models or on changes in correlation.

2In the first major paper using the correlation approach, King and Wadhwani (1990) acknowledged that volatility

affects correlation (see page 20), but implemented no correction for this effect in their empirical tests.

3This application uses U.S. dollar returns because they represent profits of investors with international portfolios

and two-days rolling averages in order to account for the fact that stock markets in different countries are not

simultaneously open. Results are robust, however, to these choices.4

Due to the rapid convergence to the normal distribution, tests for correlation coefficients are generally performed

by using their Fisherz-transformation (see Corsetti et al., 2005, for details).


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Figure 1. Number of countries experiencing stock market distress

(values, weekly data)

0

2

4

6

8

10

12

14

16

18

20

Jan-89 Jan-91 Jan-93 Jan-95 Jan-97 Jan-99 Jan-01 Jan-03 Jan-05 Jan-07 Jan-09

Source: elaborations on Thomson Reuters Datastream. The figure shows the number of countries in

our sample in which weekly returns on the stock market index recorded a decline of 20 per cent or

more with respect to the peak achieved over the previous year.

Figure 2. Volatility of stock market returns

(annualized values, weekly data)

0.00

0.10

0.20

0.30

0.40

0.50

0.60


Source: elaborations on Thomson Reuters Datastream. The bold line shows the median volatility of

weekly stock market returns in local currency; the thin-dotted lines show the first and the third

cross-sectional interquartile. Volatilities are computed as exponential moving averages with a decay

factor equal to 0.96.


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Figure 3. Covariances between stock market returns

(annualized values, weekly data)

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18


Source: elaborations on Thomson Reuters Datastream. The bold line shows the median of 190

(1019) bivariate covariances of weekly stock market returns in local currency; the thin-dotted lines

show the first and the third cross-sectional interquartile. Covariances are computed as exponential

moving averages with a decay factor equal to 0.96.

Figure 4 Correlations between stock market returns

(weekly data)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0


Source: elaborations on Thomson Reuters Datastream. The bold line shows the median of 190

(1019) bivariate correlation coefficients of weekly stock market returns in local currency; the thin-

dotted lines show the first and the third cross-sectional interquartile. Correlation coefficients are

computed as exponential moving averages with a decay factor equal to 0.96.

[2010] Correlation Analysis of Financial Contagion

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